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Semenov [28]
3 years ago
13

The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 136 feet, what is the length of the

rectangle?
Mathematics
2 answers:
Goshia [24]3 years ago
8 0
Add the ratios 3:1 = 4
divide perimeter 128 by 4 = 32
multiply this by each ratio so 3:1 becomes 96length:32width
remember there are two lengths and two widths in the perimeter so divide by 2 to find the length = 48
Elodia [21]3 years ago
8 0

Answer:  The length of the given rectangle is 51 feet.

Step-by-step explanation:  Given that the ratio of length to width in a rectangle is 3 to 1 and the perimeter of the rectangle is 136 feet.

We are to find the length of the rectangle.

Let the length and breadth of the rectangle be 3x feet and 1x feet respectively.

Then, according to the given information, we have

2(3x+1x)=136\\\\\Rightarrow 2\times4x=136\\\\\Rightarrow 8x=136\\\\\Rightarrow x=\dfrac{136}{8}\\\\\Rightarrow x=17.

Therefore, width = 17 feet and length = 17 × 3 = 51 feet.

Thus, the length of the given rectangle is 51 feet.

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Answer:

-6

Step-by-step explanation:

h(x) = -3x – 12 becomes h(-2) =  -3(-2) – 12 = -6

7 0
3 years ago
The scores on a quiz are normally distributed. The mean of the quiz is 93 and the standard deviation is 4.2. By using the Empiri
xz_007 [3.2K]

Answer:

any score that lies between 88.8 and 97.2 is within one std. dev. of the mean

Step-by-step explanation:

One std. dev. above the mean would be 93 + 4.2, or 97.2.  One std. dev. below the mean would be 93 - 4.2, or 88.8.

So:  any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.

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3 years ago
5x-3x(26x-7x-28x) systems of equation
labwork [276]

Simplifying
5x + 2(8x + -9) = 3(x + 4) + -5(2x + 7)

Reorder the terms:
5x + 2(-9 + 8x) = 3(x + 4) + -5(2x + 7)
5x + (-9 * 2 + 8x * 2) = 3(x + 4) + -5(2x + 7)
5x + (-18 + 16x) = 3(x + 4) + -5(2x + 7)

Reorder the terms:
-18 + 5x + 16x = 3(x + 4) + -5(2x + 7)

Combine like terms: 5x + 16x = 21x
-18 + 21x = 3(x + 4) + -5(2x + 7)

Reorder the terms:
-18 + 21x = 3(4 + x) + -5(2x + 7)
-18 + 21x = (4 * 3 + x * 3) + -5(2x + 7)
-18 + 21x = (12 + 3x) + -5(2x + 7)

Reorder the terms:
-18 + 21x = 12 + 3x + -5(7 + 2x)
-18 + 21x = 12 + 3x + (7 * -5 + 2x * -5)
-18 + 21x = 12 + 3x + (-35 + -10x)

Reorder the terms:
-18 + 21x = 12 + -35 + 3x + -10x

Combine like terms: 12 + -35 = -23
-18 + 21x = -23 + 3x + -10x

Combine like terms: 3x + -10x = -7x
-18 + 21x = -23 + -7x

Solving
-18 + 21x = -23 + -7x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '7x' to each side of the equation.
-18 + 21x + 7x = -23 + -7x + 7x

Combine like terms: 21x + 7x = 28x
-18 + 28x = -23 + -7x + 7x

Combine like terms: -7x + 7x = 0
-18 + 28x = -23 + 0
-18 + 28x = -23

Add '18' to each side of the equation.
-18 + 18 + 28x = -23 + 18

Combine like terms: -18 + 18 = 0
0 + 28x = -23 + 18
28x = -23 + 18

Combine like terms: -23 + 18 = -5
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Divide each side by '28'.
x = -0.1785714286

Simplifying
x = -0.1785714286
3 0
3 years ago
The functions f and g are defined by f: x = 4 - x and g: x = hx² + k. If the composite function gf is given by gf: x + 2x² - 16x
kozerog [31]

Answer:

Step-by-step explanation:

f(x) = 4-x

g(x) = hx^{2}+k

g(f(x)) = 2x^{2}-16x+26

so put  f(x)  in g(x)

h(4-x)^{2}+k

h((4-x)(4-x) + k

h(x^{2}-8x+16)+k

if h = 2 , then

2x^{2}-16x+32 + k

and we want 26  instead of 32 so subtract 6 so K = (-6)

2x^{2}-16x+32 + (-6)

2x^{2}-16x+32 - 6

2x^{2}-16x+26

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k=(-6)

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2 years ago
Jimmy borrowed $450 to start a lawn-mowing business. He charges $35 per lawn and it costs him $8 in operating costs per lawn.
Akimi4 [234]

Answer: $450

Step-by-step explanation:

Given that:

Amount borrowed = $450

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Operating cost per lawn = $8

Jimmy's cost (C(x)) :

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If x lawns are mowed :

$450 + $8 per lawn

$450 + $8x

C(x) = 450 + 8x

Intercept (value of y when x = 0

Value of C(x) ; when x = 0

C(x) = 450 + 8(0)

C(x) = 450 + 0

C(x) = 450

3 0
3 years ago
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